IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v80y2014i3p227-253.html
   My bibliography  Save this article

Decomposition approaches for block-structured chance-constrained programs with application to hydro-thermal unit commitment

Author

Listed:
  • Wim Ackooij

Abstract

The unit commitment problem, aims at computing the production schedule that satisfies the offer-demand equilibrium at minimal cost. Often such problems are considered in a deterministic framework. However uncertainty is present and non-negligible. Robustness of the production schedule is therefore a key question. In this paper, we will investigate this robustness when hydro valleys are made robust against uncertainty on inflows and the global schedule is robust against uncertainty on customer load. Both robustness requirements will be modelled by using bilateral joint chance constraints. Since this is a fairly large model, we will investigate several decomposition procedures and compare these on several typical numerical instances. The latter decomposition procedures are clearly a prerequisite if robust unit commitment is ever to be used in practice. We will show that an efficient decomposition procedure exists and can be used to derive a robust production schedule. The obtained results are illustrated on a convex simplification of a unit commitment problem in order to avoid the use of heuristics. The investigated decomposition approaches can be applied trivially to a non-convex setting, but will need to be followed by appropriate heuristics. How this may work in practice is also illustrated. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Wim Ackooij, 2014. "Decomposition approaches for block-structured chance-constrained programs with application to hydro-thermal unit commitment," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(3), pages 227-253, December.
    • Handle: RePEc:spr:mathme:v:80:y:2014:i:3:p:227-253
    DOI: 10.1007/s00186-014-0478-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-014-0478-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-014-0478-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Monique Guignard, 2003. "Lagrangean relaxation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 151-200, December.
    2. Antonio Frangioni & Claudio Gentile, 2006. "Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints," Operations Research, INFORMS, vol. 54(4), pages 767-775, August.
    3. Philpott, A. B. & Craddock, M. & Waterer, H., 2000. "Hydro-electric unit commitment subject to uncertain demand," European Journal of Operational Research, Elsevier, vol. 125(2), pages 410-424, September.
    4. N.C.P. Edirisinghe & E.I. Patterson & N. Saadouli, 2000. "Capacity Planning Model for a Multipurpose Water Reservoir with Target-Priority Operation," Annals of Operations Research, Springer, vol. 100(1), pages 273-303, December.
    5. Wim Van Ackooij & René Henrion & Andris Möller & Riadh Zorgati, 2010. "On probabilistic constraints induced by rectangular sets and multivariate normal distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 535-549, June.
    6. Arthur F. Veinott, 1967. "The Supporting Hyperplane Method for Unimodal Programming," Operations Research, INFORMS, vol. 15(1), pages 147-152, February.
    7. Wim Ackooij & Welington Oliveira, 2014. "Level bundle methods for constrained convex optimization with various oracles," Computational Optimization and Applications, Springer, vol. 57(3), pages 555-597, April.
    8. C. Beltran & F. J. Heredia, 2002. "Unit Commitment by Augmented Lagrangian Relaxation: Testing Two Decomposition Approaches," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 295-314, February.
    9. Matthias Nowak & Werner Römisch, 2000. "Stochastic Lagrangian Relaxation Applied to Power Scheduling in a Hydro-Thermal System under Uncertainty," Annals of Operations Research, Springer, vol. 100(1), pages 251-272, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wim Ackooij, 2017. "A comparison of four approaches from stochastic programming for large-scale unit-commitment," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 119-147, March.
    2. Wim Ackooij & Nicolas Lebbe & Jérôme Malick, 2017. "Regularized decomposition of large scale block-structured robust optimization problems," Computational Management Science, Springer, vol. 14(3), pages 393-421, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wim Ackooij & Jérôme Malick, 2016. "Decomposition algorithm for large-scale two-stage unit-commitment," Annals of Operations Research, Springer, vol. 238(1), pages 587-613, March.
    2. Wim Ackooij & Jérôme Malick, 2016. "Decomposition algorithm for large-scale two-stage unit-commitment," Annals of Operations Research, Springer, vol. 238(1), pages 587-613, March.
    3. Wim Ackooij, 2017. "A comparison of four approaches from stochastic programming for large-scale unit-commitment," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 119-147, March.
    4. Luis Montero & Antonio Bello & Javier Reneses, 2022. "A Review on the Unit Commitment Problem: Approaches, Techniques, and Resolution Methods," Energies, MDPI, vol. 15(4), pages 1-40, February.
    5. G. Rius-Sorolla & J. Maheut & Jairo R. Coronado-Hernandez & J. P. Garcia-Sabater, 2020. "Lagrangian relaxation of the generic materials and operations planning model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 105-123, March.
    6. Wim Ackooij & Welington Oliveira, 2014. "Level bundle methods for constrained convex optimization with various oracles," Computational Optimization and Applications, Springer, vol. 57(3), pages 555-597, April.
    7. Yonghan Feng & Sarah Ryan, 2016. "Solution sensitivity-based scenario reduction for stochastic unit commitment," Computational Management Science, Springer, vol. 13(1), pages 29-62, January.
    8. Holger Berthold & Holger Heitsch & René Henrion & Jan Schwientek, 2022. "On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 1-37, August.
    9. Maria Vespucci & Francesca Maggioni & Maria Bertocchi & Mario Innorta, 2012. "A stochastic model for the daily coordination of pumped storage hydro plants and wind power plants," Annals of Operations Research, Springer, vol. 193(1), pages 91-105, March.
    10. C. Gentile & G. Morales-España & A. Ramos, 2017. "A tight MIP formulation of the unit commitment problem with start-up and shut-down constraints," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 177-201, March.
    11. René Henrion & Andris Möller, 2012. "A Gradient Formula for Linear Chance Constraints Under Gaussian Distribution," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 475-488, August.
    12. Lisa Göransson & Caroline Granfeldt & Ann-Brith Strömberg, 2021. "Management of Wind Power Variations in Electricity System Investment Models," SN Operations Research Forum, Springer, vol. 2(2), pages 1-30, June.
    13. Hongling, Liu & Chuanwen, Jiang & Yan, Zhang, 2008. "A review on risk-constrained hydropower scheduling in deregulated power market," Renewable and Sustainable Energy Reviews, Elsevier, vol. 12(5), pages 1465-1475, June.
    14. Thomas Bittar & Pierre Carpentier & Jean-Philippe Chancelier & Jérôme Lonchampt, 2022. "A decomposition method by interaction prediction for the optimization of maintenance scheduling," Annals of Operations Research, Springer, vol. 316(1), pages 229-267, September.
    15. Quddus, Md Abdul & Shahvari, Omid & Marufuzzaman, Mohammad & Ekşioğlu, Sandra D. & Castillo-Villar, Krystel K., 2021. "Designing a reliable electric vehicle charging station expansion under uncertainty," International Journal of Production Economics, Elsevier, vol. 236(C).
    16. Schulze, Tim & McKinnon, Ken, 2016. "The value of stochastic programming in day-ahead and intra-day generation unit commitment," Energy, Elsevier, vol. 101(C), pages 592-605.
    17. Guanglei Wang & Hassan Hijazi, 2018. "Mathematical programming methods for microgrid design and operations: a survey on deterministic and stochastic approaches," Computational Optimization and Applications, Springer, vol. 71(2), pages 553-608, November.
    18. Felipe Serrano & Robert Schwarz & Ambros Gleixner, 2020. "On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm," Journal of Global Optimization, Springer, vol. 78(1), pages 161-179, September.
    19. C. Beltran-Royo, 2009. "The radar method: an effective line search for piecewise linear concave functions," Annals of Operations Research, Springer, vol. 166(1), pages 299-312, February.
    20. Fatma Kılınç-Karzan, 2016. "On Minimal Valid Inequalities for Mixed Integer Conic Programs," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 477-510, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:80:y:2014:i:3:p:227-253. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.